MOSCOW (Reuters) -- The presidents of Russia and the United States have agreed to extend talks to secure a new pact to cut vast arsenals of nuclear weapons, the Kremlin said.

U.S. President Barack Obama and his Russian counterpart, Dmitry Medvedev, agreed by telephone to continue work on finding a successor to the Cold War-era START-1 treaty after "intensive and purposeful" talks between their delegations in Geneva.

"The heads of state agreed to give the order to continue active work and not to reduce the high level and tempo of cooperation, with the aim of securing decisive agreements on all issues," the Kremlin said in a statement.

An Obama administration official said the two leaders spoke on December 12 to discuss the ongoing START negotiations, but the official had no further details.

Washington and Moscow say finding a replacement for the 1991 Strategic Arms Reduction Treaty, the biggest agreed nuclear weapons cut in history, would help "reset" relations after rows in recent years.

The countries failed to reach agreement on a successor to START-1 before this month's deadline, although the treaty will remain in force indefinitely pending agreement on a successor.

No reasons have been given for the delay. Diplomats are now talking about finding a deal by the end of the year, although it is unclear when the two presidents will sign such a pact. The Kremlin made no reference to a date in its December 12 statement.

Negotiations had been proceeding in Switzerland under unusually tight secrecy. Both parties had been committed to a news blackout on the talks, and even senior embassy staff were not fully briefed.

The START-1 treaty, signed by then-U.S. President George H.W. Bush and Soviet leader Mikhail Gorbachev, took nearly a decade to achieve. Under the deal, Russia more than halved its nuclear arsenal, the Foreign Ministry has said.

A new deal would cut the number of deployed nuclear weapons and the submarines, bombers and missiles used to launch them. But the United States and Russia would still have enough firepower to destroy the world several times over.